A spiral is a curve drawn from a fixed point steadily getting farther and farther away from the starting point.
With an Archimedean spiral the loops are spaced evenly (so if you draw a line from the center of it outwards it will cross the spiral at equal intervals) whereas with a Logarithmic spiral the loop size increases in a geometric sequence (most commonly using Fibonacci numbers so that if you draw a line from the center outwards it will cross the spiral at a distance of 1, 2, 3, 5, 8, 13...). Logarithmic Spirals using Fibonacci numbers are very commonly found in nature. I don't think I'm up to describing Fermat's Spiral, but that node has some very nice ascii art you can look at.
Also, in Football a ball passed or kicked with a spin which propels it further with more accuracy; the ball points the same direction throughout its flight. (http://www.firstbasesports.com/glossaries/ftbglos.htm)
Or a defect in the cleaved end face of an optical fiber in which the surface changes abruptly. (http://www.laurin.com/DataCenter/Dictionary/)